A hemispherical dome has a diameter of 100m. A spotlight is placed on point B along the circumference on ground level. A balloon is released at point A on the center at a rate of 2m/s. how fast is the shadow of the balloon move on the roof when the balloon is 25m high?

What have you tried so far? Also, if this is homework, you may want to add the "homework" tag.
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ArgonAug 22 '12 at 2:18

A title had better explain what the question is about. I guess with all these numbers, it looks like an assignment problem.
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FrenzY DT.Aug 22 '12 at 2:22

There will be no shadow because (i) the balloon is not high enough for the spotlight to reach it (the dome is in the way), and (ii) if the spotlight is on the ground, then it will be casting a shadow of the balloon up into space, not down onto the roof.
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ThéophileAug 22 '12 at 2:31

@Théophile I think point A is on the ground and at the center of the big circle? And we ignore diffraction.
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FrenzY DT.Aug 22 '12 at 2:34

Ah, the balloon is inside the dome? And so is the spotlight? I had understood that the balloon was released from the top of the roof. A clearer description of the problem would help! (The picture below helps a lot ...)
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ThéophileAug 22 '12 at 2:48